Least Common Multiple (LCM) of 12 and 54
The least common multiple (LCM) of 12 and 54 is 108.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 12 and 54?
First, calculate the GCD of 12 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 54 = 0 remainder 12 |
| 2 | 54 ÷ 12 = 4 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 124 | 3224 |
| 142 and 108 | 7668 |
| 115 and 177 | 20355 |
| 150 and 173 | 25950 |
| 71 and 145 | 10295 |